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<h4 class="heading"><span class="type">Paragraph</span></h4>
<p>Here we consider the following initial value problem which involves a step input function—typical of many control-type problems:</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
\ddot{x}+3\dot{x}+2x=u_0(t), \ \  x(0)=\dot{x}(0) =0. \label{Hsys}
\end{equation*}
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<p class="continuation">Here we have a second order ODE representing a system that is at rest until time <span class="process-math">\(t=0,\)</span> when a unit step input <span class="process-math">\(u_0(t)\)</span> is applied; we seek the output <span class="process-math">\(x(t).\)</span></p>
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